The energy and water appropriations bill approved by the Senate Wednesday is $440 million under President Reagan's request, although the administration contends that it exceeds Reagan's request for domestic spending by about $350 million. It was reported incorrectly yesterday that the bill exceeded Reagan's total request for the legislation by $350 million.

The Clinch River breeder reactor yesterday suffered a potentially lethal blow as the Senate joined the House in voting to block further work on the controversial nuclear power project until a new financing arrangement can be worked out by the Department of Energy.

The Senate denied the administration's request for $270 million to continue work on the reactor, which is called a breeder because it would produce more radioactive fuel than it would consume. It took that action as it approved, 91 to 6, a $14.1 billion energy and water appropriations bill for next year.

Although the Senate vote does not necessarily kill the Tennessee-based project, Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), who is its strongest supporter and who has protected it but by ever-diminishing margins in recent years, gave it no better than a "50-50 chance" for survival.

"I think the future of it is very much in doubt," added Sen. Jim Sasser (D-Tenn.), although he noted that the breeder has had a "perils of Pauline" existence over the past decade but has always managed to survive.

"The Clinch River project . . . is dying if not dead," said Sen. Gordon J. Humphrey (R-N.H.), who helped lead the fight against the breeder.

Both House and Senate versions of the energy-water appropriations bill would deny continued funding for the project, for which ground has been broken, until a new cost-sharing arrangement with private industry is worked out.

Many lawmakers are skeptical that an agreement satisfactory to Congress can be achieved, although Baker, in supporting the delay, said that such an agreement is reachable.

While denying funds for the breeder, estimated to cost at least $3.9 billion, the Senate refused, 62 to 35, to cut off an allocation of $22.3 million for the Garrison Diversion Union, a huge irrigation project in North Dakota.

In addition to wanting the money for Clinch, the administration objected to some provisions of the energy-water bill, including increased outlays for solar and other renewable energy projects, but has not threatened a veto. The bill exceeds the administration request by $350 million, excluding the breeder reactor funds.

But the Senate Appropriations Committee late yesterday approved a $34 billion agriculture appropriations bill, including feeding programs, that is patterned closely after a House version that has drawn veto threats. Aside from a supplemental money bill for the rest of this fiscal year, the agriculture measure is the first veto-threatened appropriations bill to be cleared for floor action in the Republican-controlled Senate.

Among other things, the administration charges that the legislation funds automatic programs, such as food stamps, for only part of the fiscal year, meaning that more money would eventually be required. Lawmakers counter that they are putting time limits on the funding to prevent the administration from cutting benefits when the money runs out.

The committee also approved a $1.5 billion legislative appropriations bill that is expected to trigger a floor fight over a proposal by Sen. Jake Garn (R-Utah) to limit senators' income from investments.

The Senate already has approved legislation to limit members' income from speech-making. And Garn has served notice that he will try to impose a similar limit on unearned income, contending that having no limit benefits wealthy members most.

The House, meanwhile, shrugged off veto warnings and adopted an $11.3 billion transportation appropriations bill. Republicans failed 223 to 191 to cut by 4 percent all programs not insulated by law.

The bill provides $384.9 million more than President Reagan requested but is still $507.4 million less than the fiscal 1983 measure. It includes $517.4 million more than the administration wanted for urban mass transit programs, much of it for operating subsidies and grants from gas tax revenues for such new transit systems as the proposed 18.5-mile subway for Los Angeles.